Tunable metamaterials and related devices

ABSTRACT

A tunable metamaterial comprising a membrane on which is arranged a two-dimensional array of elements to form a metamaterial, wherein the array is subdivided into blocks of multiple elements, each block being separated from adjacent blocks by a gap to allow each block to be moveable relative to its adjacent blocks. The lattice of the metamaterial and hence its properties are tuned by inducing adjacent blocks to move away from each other or towards each other either in-plane or out-of-plane in a controllable manner in response to an electrical, thermal or optical control signal.

BACKGROUND OF THE INVENTION

This invention relates to tunable metamaterials, nonlinear metamaterialsand related devices.

Switchable and tunable metamaterials are expanding areas of researchdriven by the development of nanophotonic all-optical data processingcircuits, optical memory, smart surfaces, adaptable detection, imagingsystems, and transformation optics devices [ref.1].

Several avenues are being explored. Metamaterials where metalnanostructures which support plasmons are hybridized with nonlinear andswitchable layers provide a way to achieve high-contrast opticalswitching and enhanced nonlinear responses. Indeed, a change in therefractive index or absorption in a hybridized material will modify theplasmon spectrum of the nanostructure. This can lead to a strong changein the resonant transmission and reflection characteristics of thehybrid structure. For instance the ability to change a metamaterial'sresponse at terahertz frequencies by injection or optical generation offree carriers in a semiconductor substrate has been reported [refs.2,3]. A layer of single-wall semiconductor carbon nanotubes deposited ona metamaterial shows an order of magnitude higher nonlinearity than thealready extremely strong response of the nanotubes themselves due toresonant plasmon-exciton interactions [ref. 4]. Nanoscale metamaterialelectro-optical switches using phase change chalcogenide glass [ref. 5]and vanadium dioxide [ref. 6] have already been demonstrated. Grapheneis also a popular material that promises to add electroopticalcapability to metamaterials in particular in the infrared and terahertzdomains by exploiting the spectral shift of the electromagnetic responsethat is driven by applied voltage [ref. 7,8].

When high-speed control is not needed, metamaterials can be reliably andreversibly controlled by using microelectromechanical (MEMS) actuatorsto reposition parts of the meta-molecules. MEMS-based metamaterials canprovide continuous tuning, rather than steplike switching associatedwith phase-change materials and, in contrast to approaches exploitingoptical nonlinearities, they are compatible with low intensities. Thishas been convincingly demonstrated for terahertz and far infraredmetamaterials consisting of specially designed deformable meta-molecules[refs. 9,10]. It has also been proposed to tune metamaterialsstructurally through continuous adjustment of a metamaterial's latticestructure [ref. 12]. In ref. 12, this concept is demonstrated in the GHzregion by a millimeter scale three-dimensional lattice formed by avertical stack of circuit boards, each representing a two-dimensionalmetamaterial, where the tuning is provided by laterally shifting everyother circuit board.

However, reconfigurable photonic metamaterials (RPMs) operating in thevisible and near-infrared parts of the spectrum require the developmentof components and actuators operating on the scale of a few tens ofnanometers rather than millimeters.

SUMMARY OF THE INVENTION

In one aspect, the invention provides a tunable metamaterial structurecomprising a membrane having an area that is subdivided into a pluralityof strips extending in a first dimension with neighboring strips beingspaced apart in a second dimension by gaps, wherein the area hosts ametamaterial formed by an array of metamaterial elements which at leastpartially cover the area of the strips and define a plurality of latticeparameters of the metamaterial, and wherein at least selected ones ofthe strips are shaped and dimensioned to permit their motion in responseto a control parameter, thereby to cause neighboring strips to moverelative to each other and thereby perturb at least one latticeparameter of the metamaterial. In another aspect, the invention providesa tunable metamaterial device comprising a structure as specified abovein combination with a device controller operable to set the controlparameter.

This approach has the advantage that it does not depend on the detailsof the meta-molecule design and is thus applicable to a huge range ofmetamaterial patterns.

This approach also has the advantage that it eliminates the need forreconfigurable elements on the size scale of the meta-molecules, whichwould be extremely challenging to achieve for the optical part of thespectrum.

The strips preferably have a periodicity in the second dimension matchedto a lattice parameter of the metamaterial in the second dimension. Thematching can be a one-to-one matching or some other integer ratio.

The lattice parameters of the metamaterial may be smaller than one of2000 nm, 1500 nm, 1250 nm, 1000 nm, 750 nm, 500 nm and 250 nm. Inparticular, embodiments of the invention are directed towards opticaleffects in the visible and near infra-red regions in which case bydefinition the lattice parameters of the metamaterial need to be smallerthan the wavelengths in those regions. However, wavelengths smaller thanlattice parameters may also be used, for example for operation as atunable diffraction grating.

It is therefore possible to electro-mechanically, thermally or opticallycontrol the electromagnetic properties of metamaterials in the visibleto near infrared spectral range. As the electromagnetic properties ofalmost any metamaterial depend on coupling between metamaterialresonators, control over the relative position of these resonators willlead to tuning of the metamaterial properties. In particular, controlover resonator coupling can be achieved by placing the metamaterialresonators on reconfigurable support structures that move in differentways in response to an external stimulus used as a control parameter. Inparticular, in embodiments of the invention the metamaterial resonatorsare placed on alternating reconfigurable and non-reconfigurable supportstructures or alternating support structures that move away from eachother or towards each other either in-plane or out-of-plane in acontrollable manner in response to an electrical, thermal or opticalcontrol signal.

The proposed approach allows switchable and/or tunable and/or nonlinearproperties to be added to a very large number of metamaterial devices,which could then replace the corresponding conventional opticalcomponents. Typically conventional devices that control the intensity,phase or polarization state of light are large devices that integrateweak effects over long distances in expensive crystals, for examplemodulators, polarization rotators and wave plates. Typically, tunabilityof such devices requires large additional components such as motors thatmove mechanical components or coils that generate an external magneticfield. The proposed approach will allow metamaterials of sub-wavelengththickness to be used to control and modulate the intensity, phase,polarization and frequency of light. Such metamaterial components can bemass-produced from cheap materials using standard semiconductormanufacturing techniques. They can be simply controlled by an appliedvoltage, temperature or electromagnetic wave and do not require largeexternal components such as motors or coils. Thus the proposed approachwill be particularly useful for the miniaturization of photonic devicesand the realization of photonic circuits.

Tunability will be introduced in almost any metamaterial system, if thedistance and thus the coupling between neighboring meta-molecules can becontrolled. For example, this may be achieved by placing themeta-molecules on alternating reconfigurable and nonreconfigurablesupport structures.

In some embodiments, the membrane is provided with contacts to permit atleast a subset of the strips to be electrically addressed with anelectrical actuation signal which causes relative movement betweenneighboring strips. In particular, in electrostatically actuatedembodiments, the contacts are arranged to apply mutually attractive andrepulsive electrostatic forces laterally between neighboring strips, sothat a first subset of the gaps widen and a second subset of the gapsinterleaved with the first subset narrow under application of theelectrical actuation signal. Alternatively, in electrothermally actuatedembodiments, the contacts are arranged to apply a current to at least afirst subset of the strips, and wherein at least a subset of the stripsare made of a plurality of layers of different materials with differentthermal expansion coefficients such that changes in temperature inducedby the current cause bowing of those strips out of the plane of themembrane. Electrically actuated embodiments have the advantage that theycan be realized with low operating voltages of a few volts.

In thermally actuated embodiments, at least a first subset of the stripsare made of a plurality of layers of different materials with differentthermal expansion coefficients such that changes in temperature causebowing of those strips out of the plane of the membrane.

In optically actuated embodiments an optical signal causes relativemovement of at least two subsets of strips. In particular, inoptothermally actuated embodiments, at least a first subset of thestrips are made of a plurality of layers of different materials withdifferent thermal expansion coefficients such that changes of theirtemperature cause bowing of those strips out of the plane of themembrane, and a temperature change can be caused by an appliedelectromagnetic wave.

In a further optically actuated embodiment, actuation can be byelectromagnetic forces. A first subset and a second subset of strips areat least partially covered by metamaterial elements configured to exertmutually attractive and/or repulsive lateral electromagnetic forces onone another when excited with an electromagnetic wave of an appropriatefrequency, such that a first subset of gaps widens and a second subsetof gaps interleaved with the first subset narrows under application ofthe electromagnetic wave. In either of the optically actuatedembodiments, the optical actuation signal can be an optical signal thatis manipulated by the metamaterial device, or an additional opticalcontrol signal. The latter case allows the manipulation of light withlight.

The strips may have more flexible end portions to facilitate lateralmotion of the strips in particular for the electrostatic embodiments andembodiments actuated by electromagnetic forces. The more flexible endedportions can be formed as folded structures or narrowed structures, forexample.

At least selected ones of the strips can be provided with lateralprotrusions facing into the gaps to inhibit large area contact betweenneighboring strips.

The strips can be formed as folded structures along their full length.

BRIEF DESCRIPTION OF THE DRAWINGS

This invention will now be further described, by way of example only,with reference to the accompanying drawings.

FIG. 1 is a schematic perspective view of an electrostaticallycontrolled metamaterial structure according to a first embodiment.

FIG. 2( a) shows in plan view a scanning electron micrograph of anexample structure of the first embodiment in its rest position or “OFF”state.

FIG. 2( b) corresponds to FIG. 2( a), but shows the same structure inits fully actuated position or “ON” state.

FIG. 3 is a graph showing the change in reflectivity R as a function ofwavelength when the example device is in its OFF and ON states as shownin FIGS. 2( a) and 2(b) respectively.

FIG. 4 shows a modified bridge piece in which the main central part ofthe bridge piece is connected to the support structure with waistedportions.

FIG. 5 shows a modified bridge piece in which the bridge is connected tothe support structure with waisted portions formed of concertinaportions.

FIG. 6 shows a modified bridge piece in which the whole bridge has aconcertina form.

FIG. 7 shows a further modified bridge piece similar to FIG. 4, but withlaterally extending bumps or protrusions arranged on one side surface ofthe bridge piece.

FIG. 8A-8I are schematic drawings of alternative “atom” or“meta-molecule” forms for the metamaterial structure.

FIG. 9( a) is a schematic perspective view of a thermally controlledmetamaterial structure comprising alternating bimaterial bridgesaccording to a second embodiment.

FIG. 9( b) are schematic sections of bilayered (left) and trilayered(right) support beams made of materials with different thermal expansioncoefficients used to illustrate the second embodiment.

FIG. 10( a) is a schematic perspective view of a thermally controlledreconfigurable photonic metamaterial according to the second embodiment.

FIG. 10( b) is a scanning electron micrograph corresponding to FIG. 10(a) taken at room temperature of an example metamaterial structure of thesecond embodiment.

FIG. 11( a) is a graph of transmission T as a function of wavelength forthe example metamaterial structure of FIG. 10( b).

FIG. 11( b) is a graph of the relative change in transmission T as afunction of wavelength at six different temperatures normalized to areference temperature of 76 K for the example metamaterial structure ofFIG. 10( b).

FIG. 12 is a schematic perspective view of an electrothermallycontrolled metamaterial structure according to a third embodiment.

FIG. 13 is a schematic view of an electromagnetically controlledmetamaterial structure according to a fourth embodiment.

FIG. 14 is a schematic depiction of a temperature sensor including ametamaterial structure according to embodiments of the invention.

FIGS. 15 a and 15 b are schematic depictions of electro-optic switchesbased on metamaterial structures according to embodiments of theinvention.

FIGS. 16 a and 16 b are schematic depictions of electro-optic modulatorsbased on metamaterial structures according to embodiments of theinvention.

FIGS. 17 a and 17 b are schematic depictions of tunable polarizationrotators based on metamaterial structures according to embodiments ofthe invention.

FIGS. 18 a and 18 b are schematic depictions of tunable polarizationspectral filters based on metamaterial structures according toembodiments of the invention.

FIGS. 19 a, 19 b and 19 c are schematic depictions of tunable waveplates based on metamaterial structures according to embodiments of theinvention.

FIGS. 20 a, 20 b and 20 c are schematic depictions of tunable modulators(or switches) based on electromagnetically controlled metamaterialstructures according to embodiments of the invention.

FIGS. 21 a and 21 b are schematic depictions of tunable diffractiongratings based on metamaterial structures according to embodiments ofthe invention.

DETAILED DESCRIPTION

A first embodiment is now described.

FIG. 1 is a schematic perspective view of an electrostaticallycontrolled metamaterial structure according to a first embodiment. Theillustrated part is a free standing relatively thin layer of material10, for example a membrane formed by conventional MEMS techniques byetching a thicker substrate. At least part of the material 10 iselectrically conductive, for example due to presence of an electricallyconductive coating such as an alloy or metal (such as gold) or atransparent conducting oxide (such as indium tin oxide). By relativelythin, it is meant sufficiently thin to display the electrically actuatedelastic deformation properties described below. The thin layer ormembrane 10 has an area which hosts a metamaterial defined by first andsecond end supports 12, 14 between which are formed a plurality ofstrips or bridge pieces 16 which extend parallel to each other in thex-direction. Each bridge piece 16 is separated in the y-direction fromits adjacent or neighboring bridge piece by a gap formed by a slit orslot. It will be understood that these gaps can be formed in a solidmembrane by etching or milling using conventional semiconductorfabrication techniques.

A metamaterial is formed over the membrane 10 and specifically over atleast part of the area covered by the bridge pieces 16. Each “atom” or“molecule” 18 of the metamaterial “lattice” is indicated with thesquares with rounded corners. A plurality of meta-molecules is arrangedalong each bridge piece having a characteristic separation in thex-direction. The neighboring meta-molecules on adjacent bridge piecesalso have a characteristic separation in the y-direction, therebyforming a two-dimensional (2D) lattice. The x- and y-separations couldbe the same as illustrated, or could be different. Moreover, the squaregrid shown could instead be a hexagonal close packed grid, i.e. comparedto the illustration the meta-molecules on each second bridge piece couldbe shifted in the x-direction by half a period. The meta-molecules canbe formed in a conventional manner, e.g. by structuring a metallic film.Materials and structure options for forming the metamaterial arediscussed further below.

A plurality of first and second bridge-specific electrical disconnects20, 22 (for example gaps in the electrically conductive layer) arearranged on the first and second end supports 12, 14 respectively at thejunction between the end support and the bridge piece, so that first andsecond subsets of bridge pieces are only contacted on one end. The firstsubset of bridge pieces is electrically connected to the first endsupport which is connected to a positive voltage terminal and the secondsubset of bridge pieces is electrically connected to the second endsupport which is connected to a negative voltage terminal. Theelectrical disconnects 20, 22 are arranged so that oppositely chargedpotentials can be applied to neighboring bridge pieces 16 so that thoseneighboring bridge pieces will attract (or repel) each other whenpotentials of the opposite (or the same) sign are applied via the endsupports. In the illustrated example, the first and second electricaldisconnects are arranged in alternating pairs along the rows of bridgepieces. The attractive and repulsive forces generated electrostaticallyare sufficiently strong to displace the bridge pieces in the y-directionas schematically indicated with the arrows, thereby widening and closingthe gaps alternately from row to row. This has the effect of alteringthe metamaterial lattice, since it changes the y-separation betweenmeta-molecules. It is this property that leads to the tunable devicefunction. The effect is reversible, since the displacement of the bridgepieces is by elastic deformation, so a restoring force exists which isproportional to the y-displacement, while the electrostatic forcebetween bridge pieces grows infinite as their separation approacheszero. The application of an electrostatic potential will thereforeresult in a switching behavior when the electrostatic attraction betweenneighboring bridge pieces overcomes the elastic restoring force, leadingto a step change in the metamaterial's electromagnetic properties over ashort range of applied voltage. In other devices, a continuous tuningrange may be preferred. The elastic properties of the bridge pieces, thegap width and other parameters may be chosen to promote either a binaryswitching type operation or operation based on a continuous variation ofthe gap with applied voltage.

FIG. 2( a) shows in plan view a scanning electron micrograph of anexample structure of the first embodiment in its rest position or “OFF”state. FIG. 2( b) corresponds to FIG. 2( a), but shows the samestructure in its fully actuated position or “ON” state. This example ofan electrically controlled reconfigurable photonic metamaterial has 35nm long silicon nitride bridges alternatingly covered with eithernanoscale “fishscale”-shaped plasmonic resonators 16 a or continuousgold wires 16 b. The “fishscale”-shaped plasmonic resonators 16 a areformed of a meandering metal track of width in the y-direction of 150 nmfor the y-extending portions and a width of 100 nm in the x-directionfor the x-extending portions. The meanders have a 800 nm period in thex-direction. The gold wires 16 b have a width of 260 nm. The entirestructure was fabricated by focused ion beam milling from a 50 nm thicksilicon nitride membrane covered by a 50 nm thick thermally evaporatedgold layer. The bridge pieces were separated by 125 nm gaps forelectrical isolation and pairs of bridges were alternatingly connectedto two electrical contacts for electrostatic control of the device. Avoltage applied to the metamaterial device leads to alternatingattractive and repulsive electrostatic forces between “fishscale” and“wire”-bridges. At small voltages the electrostatic forces are inequilibrium with the restoring force of the elastic bridges leading toonly small displacements. However, as the restoring force isproportional to the bridge displacement, while the electrostatic forcesbecome infinite when the bridge separation approaches zero, there is athreshold voltage where the electrostatic force overcomes the restoringforce. At the threshold voltage, the structure switches into abridge-pair configuration, compare FIGS. 2( a) and (b), showing the“off” and “on”-states respectively. In this example, the thresholdvoltage U_(th)=5.7 V.

FIG. 3 is a graph showing the change in reflectivity R as a function ofwavelength when the example device is in its OFF and ON states as shownin FIGS. 2( a) and 2(b) respectively. As can be seen from the graph,switching of the metamaterial state leads to dramatic changes of themetamaterial's reflection properties. Switching the metamaterial to its“on”-state by applying a voltage above U_(th) increases its reflectivityby 72% in the telecommunications band around 1.5 μm. This large changein reflectivity is linked to a resonant mode of the coupled system offishscale structure and straight wires. The resonant properties of thissystem strongly depend on coupling between neighboring bridges andswitching the metamaterial to its “on”-state red-shifts the resonance byabout 15% as the plasmonic structures are moved together byelectrostatic forces.

FIG. 4 shows a modified bridge piece 16 in which the main central partof the bridge piece is connected to the two sides of the supportstructure 12, 14 with first and second waisted portions 24, 26. Thewaisted, narrowed or thinned portions 24, 26 may be thinned relative tothe central part of the bridge only in the y-dimension visible in theschematic plan view, or optionally also in the depth or z-dimension. Anelectrical disconnect 22 is also shown. These structurally modified endportions facilitate easier movement of the bridge structure in responseto the external electrical, thermal or optical (electromagnetic)stimulus. For example, the ends of the bridges can have a reduced widthwithin the metamaterial plane as illustrated to make it easier for thestructure to bend within the metamaterial plane.

FIG. 5 shows a modified bridge piece 16 in which the bridge is connectedto the support structure 12, 14 with waisted portions 24, 26 formed ofconcertina portions capable of changing their length and also ofallowing lateral displacement between their ends, with little force. Anelectrical disconnect 22 is also shown. As shown in this figure, theshape of the bridge-to-support connecting parts may be modified tofacilitate easier bending and stretching. As illustrated, a concertinaor spring-like meandering structure can be used for the end parts of thebridges. It would also be possible to provide a special end bridgeportion of the kind shown in FIG. 4 and FIG. 5 only at one end.

FIG. 6 shows a modified bridge piece in which the whole bridge 16 has aconcertina form. In this case the pitch of the spring or concertinastructure, i.e. the x-period of its folds, may also be matched to, ortake on the role of, the metamaterial resonator. The reference numeralsfollow those of previous figures for corresponding parts.

FIG. 7 shows a further modified bridge piece similar to FIG. 4, but withlaterally extending bumps or protrusions 28 arranged on one side surfaceof the bridge piece. Alternatively, the bumps could be arranged on bothside surfaces in which case only every other bridge piece would need tobe provided with the bumps. The bumps 28 extend outwards from the bridgewithin the metamaterial plane in one or in several places. Inparticular, they can fulfill the following roles:

-   -   define a minimum bridge separation;    -   prevent electrical short-circuits in electrostatically tunable        metamaterial in the case that the bumps are made from        non-conducting material; and    -   prevent neighboring bridges from joining or sticking together        which could otherwise happen in electrostatically or        electromagnetically (optically) tunable metamaterials if the        electrostatic/electromagnetic forces overcome the elastic        restoring force of the bridges (electromagnetically tunable        embodiments of the invention are described later).

It will be understood that the bumps could also be provided with abridge piece of the type shown in FIG. 5 or other bridge forms, not onlythe one illustrated in FIG. 7.

FIG. 8A-8I are schematic drawings of alternative “atom” or“meta-molecule” forms for the metamaterial structure. Each pattern mayexist in equivalent “positive” and “negative” forms. For example, in thecase of FIG. 8A, the positive form may be a 2D array of conductive wireportions deposited on an insulating substrate, whereas the correspondingnegative form is made of slits in a plasmonic film having the samepositions as the wires in the positive form. Usually “wire” versionswill require a substrate for support, whereas the slit versions can beimplemented either on a supporting substrate or as self-supporting metalor degenerate semiconductor structures without a substrate.

The alternative “atom” or “meta-molecule” forms in FIGS. 8A-8I are:

A Slit or wire dipole resonator

B Pair of wires or slits of different lengths

C “C”-shaped resonator

D Split ring

E Symmetrically split ring

F Asymmetrically split ring

G Double split ring

H Omega particle

I Fishscale element

The “atoms” or “meta-molecules” on the same bridge may be spaced or maytouch. In particular, the forms in FIGS. 8A and 8I may touch to formcontinuous metal wires or continuous slits.

The “atoms” or “meta-molecules” themselves may be arranged in a numberof different kinds of arrays. The figures relating to the abovedescribed embodiments show a square array with a one-to-one mapping ofarray row to bridge piece. A wide variety of choices is howeverpossible. For example, multiple rows may be provided on each bridgepiece. Moreover, the alignment of features between adjacent rows/bridgesmay be staggered, for example a hexagonal close-packed array could beused so that the “atoms” or “meta-molecules” of adjacent rows areoffset. Furthermore, the metamaterial structure may be formed by morethan one type of “atoms”, for example alternating rows of two “atoms”with different shape, structure or orientation may be used.

Examples of plasmonic materials that are suitable for implementing theinvention are: gold, silver, aluminum, copper or an alloy of one or moreof these metals that may contain further metal(s). Moreover, transparentconducting oxides, such as indium tin oxide, fluorine doped tin oxide(FTO) or doped zinc oxide. Graphene may also be used.

Examples of suitable dielectrics for the bridge pieces and adjacentstructure include: silica, silicon nitride and various polymers.

Various other materials may also be used as part of the overallstructure including:

-   -   Semiconductors (e.g. silicon, gallium arsenide, germanium, . . .        )    -   Gain media (e.g. erbium doped glass, quantum dots, . . . )    -   Non-linear material    -   Switchable media    -   Phase-change material (e.g. gallium lanthanum sulfide—GLS)    -   Stretchable/elastic material

To summarize, the structure of the first embodiment comprises two ormore species of alternating bridges. At least two species of bridges areelectrically conductive and electrically connected to the supportstructures on opposite sides, so that different electric potentials canbe applied to these two species of bridges. At least one species ofbridges deforms within the metamaterial plane due to attractive and/orrepulsive electrostatic forces resulting from an applied electricpotential difference (voltage). The structure can be controlled by DC,AC or otherwise modulated voltages. The species of bridges can differ,for example with respect to: their number of layers, constituentmaterials, layer thicknesses and their shape and structuring.

A second embodiment is now described.

FIG. 9( a) is a schematic perspective view of a thermally controllablemetamaterial structure according to a second embodiment. The illustratedpart is a free standing relatively thin layer of material 10, forexample a membrane formed by conventional MEMS techniques by etching athicker substrate. By relatively thin, it is meant sufficiently thin todisplay the thermally actuated elastic deformation properties describedbelow. The thin layer or membrane 10 has first and second end supports12, 14 between which are formed a plurality of bridge pieces 16 c, 16 dwhich extend parallel to each other in the x-direction. Each bridgepiece 16 c, 16 d is separated in the y-direction from its adjacent orneighboring bridge piece by a gap or slot. It will be understood thatthese gaps can be formed in a solid membrane by etching or milling usingconventional semiconductor fabrication techniques.

A metamaterial is formed over the membrane 10 and specifically over atleast part of the area covered by the bridge pieces 16 c, 16 d. Each“atom” or “molecule” 18 of the metamaterial “lattice” is indicated withthe squares with rounded corners. A plurality of meta-molecules isarranged along each bridge piece having a characteristic separation inthe x-direction. The neighboring meta-molecules on adjacent bridgepieces also have a characteristic separation in the y-direction, therebyforming a two-dimensional (2D) lattice. The x- and y-separations couldbe the same as illustrated, or could be different. Moreover, the squaregrid shown could instead be a hexagonal close packed grid, i.e. comparedto the illustration the meta-molecules on each second bridge piece couldbe shifted in the x-direction by half a period. The meta-molecules canbe formed in a conventional manner, e.g. by structuring a metallic film.Materials and structure options for forming the metamaterial arediscussed further below. In this embodiment, the thermally tunablemetamaterial support structure comprises alternating reconfigurable andnonreconfigurable bimaterial bridges.

FIG. 9( b) are schematic sections of bilayered (left) and trilayered(right) bimaterial support beams which form the bridges 16 d and 16 crespectively. Each beam 16 c, 16 d is made of two materials, one with alarge thermal expansion coefficient (shown light), e.g. gold or anotherplasmonic material, and the other with a small thermal expansioncoefficient (shown dark), e.g., silicon nitride or another dielectricmaterial. The bilayer support beams illustrated on the left side willbend in response to temperature changes. Heating is shown by the shadedarrow and cooling by the non-shaded arrow. Similar arrows are alsoincluded in FIG. 9( a). By contrast, the trilayered support beams shownon the right side of the figure do not exhibit thermally induced bendingsince there are equal contributions from the large thermal expansioncoefficient material above and below the low thermal expansion material.Bending of the bimaterial structure is thus caused by differentialthermal expansion of the constituent materials. On the other hand,nonreconfigurable support structures are provided by using a symmetricsequence of layers such as a metal-dielectric-metal three-layerstructure as illustrated.

Heating or cooling the device therefore changes the lattice of themetamaterial by changing the separation between meta-molecules inneighboring bridge pieces which will tend to change properties of thesystem, in particular resonant properties, which depend on couplingbetween neighboring bridge pieces. Heating or cooling can be achieved byany convenient method, such as control of the ambient temperature, orapplication of an electromagnetic wave (including optical frequencies).

In alternative forms, the non-deforming beams 16 c could be made of anyother symmetric layer sequence to avoid thermally induced bending. Inother alternatives the beams 16 c could be inverted bilayered beams madeto bow oppositely in response to temperature changes compared with thebeams 16 d. A further alternative would be to form the non-bowing beams16 c out of a single material type, such as a dielectric.

FIG. 10( a) is a schematic perspective view of an example thermallycontrolled reconfigurable photonic metamaterial of the secondembodiment. The metamaterial is made of nanoscale “C”- shaped apertureplasmonic resonators (split rings) supported by alternating thermallyreconfigurable and nonreconfigurable bridges. Because of the patternedand unpatterned gold layers on their front and back, the“non-reconfigurable” support structures will bend slightly in theopposite direction to the “reconfigurable” support structures inresponse to changes of the ambient temperature. The entire structure wasfabricated by focused ion beam milling from a 100 nm thick siliconnitride membrane covered by 50 nm thick thermally evaporated gold layerson both sides. In order to create reconfigurable and nonreconfigurablesupport structures, the gold underlayer was removed from every secondbridge. Next the “C”-slit plasmonic resonator pattern was milled intothe gold layer covering the front of the membrane. Finally themetamaterial membrane was cut into 50 μm long and 490 nm wide bridgesseparated by 110 nm gaps.

FIG. 10( b) is a corresponding scanning electron micrograph taken atroom temperature of the example structure. Because of the large thermalexpansion coefficient of gold (14.4×10⁻⁶/K), which exceeds that ofsilicon nitride (2.8×10⁻⁶ /K) by a factor of 5, the metamaterial bridgeswithout gold underlayer will arch upward (downward) upon heating(cooling) [ref. 11] as can be seen by the lowered bridges in thescanning electron micrograph. On the other hand, thermal bending issuppressed for the more symmetric bridges with gold underlayer, whichare raised in the scanning electron micrograph. The metamaterialproperties are position-dependent toward the end of the supportstructures, where the spacing between the metamaterial resonatorsgradually decreases. Therefore the results are taken from the centralportion of the structure, which is relatively homogeneous andexperiences the largest temperature-dependent changes.

FIG. 11( a) is a graph of transmission T as a function of wavelength forthe metamaterial for waves polarized perpendicular to the supportingbeams.

FIG. 11( b) is a graph of the relative change in transmission T as afunction of wavelength for waves polarized perpendicular to thesupporting beams, with each trace representing a different metamaterialtemperature. Each trace shows the change in transmission relative to areference temperature of 76 K.

The metamaterial's temperature-dependent transmission spectrum wasmeasured using a microspectrophotometer (CRAIC Technologies) equippedwith a cryostatic sample stage. It reveals that the structure hasresonant transmission minima in the near-infrared at about 1140, 1400,and 1670 nm. The resonant modes themselves are quite complex excitationsof the coupled system of “C”-slit resonators and the gold underlayer onevery second bridge. Importantly, the resonant properties of this systemstrongly depend on the coupling between neighboring bridges andtherefore a continuous change of the physical configuration of thenanostructure drives a dramatic change of its optical properties.

FIG. 11( b) shows the change of the reconfigurable metamaterial'stransmission characteristics at various values of temperature, eachshown relative to a reference temperature of 76 K. As the metamaterialis heated to 270 K, we observe dramatic 37, 38, and 51% relativeincreases of its transmission near its resonant transmission minima at1180, 1435, and 1735 nm, respectively. These remarkably large relativeincreases in transmission are due to a 20 nm blue shift of themetamaterial spectrum combined with an overall transmission increase asthe plasmonic resonators are moved closer together by differentialthermal expansion driven by the ambient temperature increase.Importantly, as the structure is cooled back to its initial temperatureof 76 K these changes of its transmission spectrum are reversed,indicating that the reconfigurable metamaterial returned to its initialstate.

For practical applications, it may be important to achieve a large rangetuning of the metamaterial properties with a much smaller temperaturechange. This may be achieved with longer and thinner reconfigurablesupport structures and optimized material choices and layer thicknesses,as the mechanical tuning range of the reconfigurable bimaterial beams isproportional to ΔTΔαLt, where ΔT and Δα are the temperature and thermalexpansion coefficient differences and L/t is the length/thickness aspectratio of the support structures. We chose gold for its good plasmonicproperties and silicon nitride for its easy availability in form ofmembranes of nanoscale thickness. However, silicon nitride could bereplaced by glass, which has a significantly smaller thermal expansioncoefficient of only 0.4×10⁻⁶/K [ref. 11]. Furthermore,intermetamolecular coupling could be enhanced by placing the supportingbeams closer together and the relative thermal displacement ofneighboring resonators could be doubled by alternatingmetal-on-dielectric and dielectric-on-metal reconfigurable structures,which would bend in opposite directions.

In summary of the second embodiment, it uses metal-dielectric films ofnanoscale thickness to provide a generic platform for achievinglarge-range continuous reversible tuning of metamaterial properties inthe optical part of the spectrum. By placing metamaterial resonators(meta-molecules) on a thermally reconfigurable bimaterial structure itis possible to control intermetamolecular coupling leading to areversible change of the metamaterial's transmission. In a specificexample, relative transmission changes of up to 50% have been observed.Moreover, the various generalization and materials choices describedabove in relation to the first embodiment apply also to the secondembodiment. The structure comprises two or more species of alternatingbridges, which deform differently out of the metamaterial plane inresponse to temperature changes. Deformation in at least one species ofbridges is caused by differential thermal expansion between two or moreconstituent materials. The structure can be controlled by the ambienttemperature or by heat delivered by an electromagnetic wave (opticalcontrol). The species of bridges can differ, for example with respectto: their number of layers, constituent materials, layer thicknesses andtheir shape and structuring.

A third embodiment is now described.

FIG. 12 is a schematic perspective view of an electrothermallycontrollable metamaterial structure according to the third embodiment.The illustrated part is a free standing relatively thin layer ofmaterial 10, for example a membrane formed by conventional MEMStechniques by etching a thicker substrate. By relatively thin, it ismeant sufficiently thin to display the thermally actuated elasticdeformation properties described below. The thin layer or membrane 10has first and second end supports 12, 14 between which are formed aplurality of bridge pieces 16 c, 16 d which extend parallel to eachother in the x-direction. Each bridge piece 16 c, 16 d is separated inthe y-direction from its adjacent or neighboring bridge piece by a gapor slot. It will be understood that these gaps can be formed in a solidmembrane by etching or milling using conventional semiconductorfabrication techniques.

A metamaterial is formed over the membrane 10 and specifically over atleast part of the area covered by the bridge pieces 16 c, 16 d. Each“atom” or “molecule” 18 of the metamaterial “lattice” is indicated withthe squares with rounded corners. A plurality of meta-molecules isarranged along each bridge piece having a characteristic separation inthe x-direction. The neighboring meta-molecules on adjacent bridgepieces also have a characteristic separation in the y-direction, therebyforming a two-dimensional (2D) lattice.

In this embodiment, the electrothermally tunable metamaterial supportstructure comprises alternating reconfigurable bridges 16 d andnonreconfigurable bridges 16 c.

The structure of at least one of the bridge types (preferably thereconfigurable bridges 16 d), includes one or more electricallyconductive layers (for example a metal or a transparent conductingoxide), which can be heated by currents flowing through the electricallyconductive layer(s) applied by contacts to the end supports 12, 14 via acurrent source or voltage source.

The electrothermally reconfigurable support structures 16 d are made oftwo or more layers of materials with different thermal expansioncoefficients. Bending or bowing of the beams 16 d is induced when thestructure is heated by currents flowing through the electricallyconductive layer(s) of the same and/or nearby bridges.

In the illustrated example, the electrically conductive link between theend supports and the non-deforming beams 16 c is broken by spacing areas20, 22 at the junction between the end supports and the bridge pieces 16c. Current is therefore prevented from flowing along bridges 16 c, sothese bridges are not subjected to electrically induced heating. Thebeams 16 c can then be made of the same structure as beams 16 d.Alternatively, the non-deforming beams can be made of a structure whichwill not deform when heated. This can be achieved by making thenon-deforming beams out of a single layer or a symmetric sequence oflayers so that there is no bending out of the metamaterial plane inresponse to temperature changes.

In another alternative form, the beams 16 c and 16 d may bend inopposite directions, for example by using inverted layer sequences, suchas metal on dielectric and dielectric on metal.

To summarize, the structure of the third embodiment comprises two ormore species of alternating bridges. At least one species of bridges iselectrically conductive and can be heated by electrical currents passingthrough it. At least one species of bridges deforms out of themetamaterial plane in response to temperature changes due todifferential thermal expansion between two or more constituentmaterials. The structure can be controlled by DC, AC or otherwisemodulated currents. The species of bridges can differ, for example withrespect to: their number of layers, constituent materials, layerthicknesses and their shape and structuring. Moreover, the variousgeneralization and materials choices described above in relation to thefirst embodiment apply also to the third embodiment.

A fourth embodiment is now described.

FIG. 13( a) is a schematic view of an optically (electromagnetically)controllable metamaterial structure according to a fourth embodiment.The illustrated part is a free standing relatively thin layer ofmaterial 10, for example a membrane formed by conventional MEMStechniques by etching a thicker substrate. By relatively thin, it ismeant sufficiently thin to display the optically actuated elasticdeformation properties described below. The thin layer or membrane 10has first and second end supports 12, 14 between which are formed aplurality of bridge pieces 16 e, 16 f which extend parallel to eachother in the x-direction. Each bridge piece 16 e, 16 f is separated inthe y-direction from its adjacent or neighboring bridge piece by a gapor slot. It will be understood that these gaps can be formed in a solidmembrane by etching or milling using conventional semiconductorfabrication techniques.

A metamaterial is formed over the membrane 10 and specifically over atleast part of the area covered by the bridge pieces 16 e, 16 f. Each“atom” or “molecule” 18 of the metamaterial “lattice” is indicated withthe squares with rounded corners. A plurality of meta-molecules isarranged along each bridge piece having a characteristic separation inthe x-direction. The neighboring meta-molecules on adjacent bridgepieces also have a characteristic separation in the y-direction, therebyforming a two-dimensional (2D) lattice. Each meta-molecule is aplasmonic resonator.

In this embodiment, the optically tunable metamaterial support structurecomprises alternating reconfigurable bridges 16 e and 16 f.

Charge oscillations can be excited within the plasmonic resonators by anincident electromagnetic wave. The electromagnetic wave can be adedicated electromagnetic control signal such as an optical wave appliedto the metamaterial structure, or it may be an incident optical signalwhich it is intended that the metamaterial structure will manipulate(see, for example, possible optical devices for manipulation of opticalsignals shown in FIGS. 14-21 described below). This latter alternativeis attractively simple since no additional external stimulus is requiredfor tuning. The charge oscillations are associated with opticallyinduced currents and charges which lead to attractive and/or repulsiveelectromagnetic forces between neighbouring bridges, which control thespacing between the bridges in the plane of the membrane. (For pairs offixed plasmonic resonators, such forces have been studied numerically inref. 13.) If there is a net electromagnetic force on at least one groupof bridges, the structure is tuned by the action of the appliedelectromagnetic wave. In order to produce a net electromagnetic force onat least one family of bridges, the plane containing the directionnormal to the metamaterial plane and the center line of one of saidbridges must not be a mirror plane of the structure. This can beachieved by having different plasmonic resonators (“atoms”) on adjacentbridges, or by having bridges with the same resonator type that arespaced apart by gaps that are alternately large and small, or bycombinations of these arrangements.

FIGS. 13( b) to 13(e) show examples of suitable unit cell arrangements,shown as pairs of plasmonic resonators 18 on neighboring bridges 16 e,16 f FIG. 13( b) shows identical right-side-up and up-side-downplasmonic resonators without two-fold rotational symmetry on otherwiseidentical neighboring bridges. FIG. 13( c) shows different plasmonicresonators, at least one of which does not have two-fold rotationalsymmetry, on otherwise identical bridges. FIG. 13( d) shows identicalplasmonic resonators on identical bridges, where the gaps in between thebridges are alternately small and large. FIG. 13( e) shows differentplasmonic resonators on identical bridges, where the gaps in between thebridges are alternately small and large. In all cases the plasmonicresonators can be realized as wires consisting of a plasmonic materialor as apertures in a film consisting of a plasmonic material.

To summarize, the structure of the fourth embodiment comprises two ormore species of alternating bridges. For at least one species of bridge,optical excitation of its plasmonic resonators leads to a netelectromagnetic force between said bridges and the neighboring bridges.As a result, at least one species of bridge deforms within themetamaterial plane in response to an electromagnetic wave incident onthe structure. The structure can be controlled by an optical controlsignal or by an optical signal that the structure is intended tomanipulate. Such optical signals can be continuous, pulsed or otherwisemodulated. The species of bridges can differ, for example with respectto: their number of layers, constituent materials, layer thicknesses andtheir shape, width and structuring. Moreover, the various generalizationand materials choices described above in relation to the firstembodiment apply also to the fourth embodiment.

In summary of the above-described embodiments, metamaterial resonatorsare placed on alternating reconfigurable and non-reconfigurable supportstructures or alternating support structures that move away from eachother or towards each other either in-plane (first and fourthembodiment) or out-of-plane (second and third embodiments) in acontrollable manner in response to an electrical control signal (firstand third embodiments) or a thermal control signal (second embodiment)or an electromagnetic control signal (fourth embodiment). The thermalcontrol signal of the second embodiment may be delivered by anelectromagnetic wave. These reconfigurable photonic metamaterialsprovide a flexible platform for the realization of tunable metamaterialsfor the optical part of the spectrum. By placing nanoscale plasmonicresonators with useful functionalities at optical frequencies onreconfigurable support structures, their interaction can be controlled,which leads to large-range tunability of the system's electromagneticproperties. Potential applications of this generic approach includeoptical temperature sensors, tunable spectral filters, switches,modulators and any other planar metamaterial device where tunability isrequired or desirable. Reconfigurable photonic metamaterials can beprototyped by focused ion beam milling or electron beam lithography andcould be mass-produced by standard semiconductor manufacturingtechniques.

Some example applications of the above-described structures are nowdescribed.

Metamaterial structures according to the various embodiments describedthus far can be utilized in a wide range of optical and optoelectronicdevices, such as measurement and sensing devices, and devices formodifying or modulating properties and characteristics of an opticalbeam.

FIG. 14 is a schematic depiction of a first example device. In thisexample, a metamaterial structure 40 is configured for thermal tuning,and is utilized in a temperature sensor. An optical source 42 such as alaser emits an input beam I which is incident on the metamaterialstructure 40. The beam is wholly or partially transmitted through thestructure, and the resulting output beam O is collected by a detector 44such as a photodetector or a spectrometer. Any changes in temperaturewill tune the transmission characteristics of the metamaterial structure40, so that the output beam O is modified. Analysis of the output beam Oas detected by the detector 44, compared with the input beam, can thusyield a measurement of the temperature at the location of the structure40. The individual components can be positioned far apart if desired, sothat remote temperature sensing can be carried out. Also, the sensorcould be arranged so that a reflected output beam O is detected.

The arrangement shown in FIG. 14 can also be used to measure theintensity of the input beam I, if the input beam is of sufficiently highintensity to either control the temperature of the metamaterialstructure 40 (configured for thermal tuning) or to deform themetamaterial 40 (configured for electromagnetic tuning) viaelectromagnetic forces between metamolecular resonators on differentbridges.

FIG. 15 a is a schematic depiction of a second example device, in whicha metamaterial structure 40 is used as an electro-optic switch. Thestructure 40 is configured as an electrically tunable structure, with anelectric control signal supplied from a source 46. The electric tuningmay be according to the first or third embodiments. As illustrated, theswitch is “on”, in that an input beam I is transmitted through thestructure to give an output beam O. By application of an appropriateelectric control signal, the transmission/reflection characteristic ofthe structure 40 can be altered so that the input beam is no longertransmitted, and the switch is turned “off”. The switch canalternatively be configured to operate in reflection, where the outputbeam O is reflected from the structure 40. This arrangement is shown inFIG. 15 b.

Similarly, a metamaterial structure can be used as an electro-opticmodulator. As with an electro-optic switch, the modulator can bearranged for operation in transmission (FIG. 16 a) or reflection (FIG.16 b). In these examples, though, an electrical control signal fromsource 46 is applied to an electrically tunable structure 40 to tune thetransmission/reflection characteristic of the structure so thatproperties such as amplitude, phase, polarization and frequency of aninput beam I incident on the structure 40 are modulated.

FIG. 17 a shows a further example device in which a metamaterialstructure 40 according to electrically tunable embodiments of theinvention is used as a tunable polarization rotator. FIG. 17 b shows asimilar device based on a thermally tunable or electromagneticallytunable metamaterial structure. In each arrangement, the metamaterialstructure is designed so that the metamaterial lacks two-fold rotationalsymmetry. The structure is positioned so that the input beam I is at anoblique incidence, and the polarization of the output beam O can becontrolled by changing the orientation of the structure 40 with respectto the input beam I, or by altering the applied electric, thermal oroptical control parameter.

FIG. 18 a shows an example device in which a metamaterial structure 40is employed to realize a tunable polarization spectral filter. Thestructure 40, which in this example is configured for electrical tuningvia an electrical control signal from a source 46, is optically active,and is placed between two crossed or substantially crossed polarizers.The input beam I passes through a first polarizer 48 a before reachingthe structure 40 and passing through a second polarizer 48 b to producean output beam O. The control signal is altered to control thetransmission characteristics as required. A temperature-tunable oroptically tunable metamaterial structure can alternatively be used, asshown in FIG. 18 b.

FIGS. 19 a-c show examples of a metamaterial structure 40 utilized as atunable wave plate. The tunable metamaterial has similar transmissionfor substantially linearly polarized eigenpolarizations. Themetamaterial structure can be arranged for use in transmission (FIGS. 19a and 19 c) or reflection (FIG. 19 b), and tuning of the waveplate canbe via an electrical control signal (FIGS. 19 a and 19 b) or bytemperature or input beam intensity (FIG. 19 c).

FIGS. 20 a-c show further example devices in which a metamaterialstructure 40 according to electromagnetically (optically) tunableembodiments of the invention is used as modulator or switch. Byapplication of a control beam C, the transmission/reflectioncharacteristic of the structure 40 can be altered so that propertiessuch as amplitude, phase, polarization and frequency of an input beam Iincident on the structure 40 are modulated. The output beam is marked O.The device can be configured to operate in transmission (FIG. 20 a) orreflection (FIG. 20 b). Realizations may also use both transmitted andreflected beams simultaneously as output beams (FIG. 20 c), and morethan one control beam could be used.

FIGS. 21 a and 21 b show further example devices in which a metamaterialstructure 40 is employed to realize a tunable diffraction grating. Theinput beam I is incident on the metamaterial structure 40 and is splitinto several diffracted beams. Zeroth order O₀ and first order O₁diffracted beam are indicated, but higher order diffracted beams mayalso exist. Tuning may be controlled by an electric control signal (FIG.21 a) or by an electromagnetic (optical) or thermal control signal (FIG.21 b) and the diffraction grating may operate in transmission (FIG. 21a) or reflection (FIG. 21 b) or both.

It is to be understood that the above-described devices are examplesonly, and the invention is not limited thereby. Other applications ofthe tunable metamaterial structures and further devices incorporatingthe structures will be apparent to the skilled person.

REFERENCES

(1) Zheludev, N. I. Opt. Photonics News 2011, 22, 30-35.

(2) Chen, H.-T.; Padilla, W. J.; Zide, J. M. O.; Gossard, A. C.; Taylor,A. J.; Averitt, R. D. Nature 2006, 444, 597-600.

(3) Kanda, N.; Konishi, K.; Kuwata-Gonokami, M. Opt. Lett. 2009, 34,3000-3002.

(4) Nikolaenko, A. E.; Angelis, F. D.; Boden, S. A.; Papasimakis, N.;Ashburn, P.; Fabrizio, E. D.; Zheludev, N. I. Phys. Rev. Lett. 2010,104, 153902.

(5) Samson, Z. L.; MacDonald, K. F.; De Angelis, F.; Gholipour, B.;Knight, K.; Huang, C.-C.; Fabrizio, E. D.; Hewak, D. W.; Zheludev, N. I.Appl. Phys. Lett. 2010, 96, 143105.

(6) Driscoll, T.; Kim, H. T.; Chae, B. G.; Kim, B. J.; Lee, Y. W.;Jokerst, N. M.; Palit, S.; Smith, D. R.; Ventra, M. D.; Basov, D. N.Science 2009, 325, 1518-1521.

(7) Wang, F.; Zhang, Y.; Tian, C.; Girit, C.; Zettl, A.; Crommie, M.;Shen, Y. R. Science 2008, 320, 206-209

(8) Zheludev, N. I. Science 2010, 328, 582-583.

(9) Tao, H.; Strikwerda, A. C.; Fan, K.; Padilla, W. J.; Zhang, X.;Averitt, R. D. Phys. Rev. Lett. 2009, 103, 147401.

(10) Zhu, W. M.; Liu, A. Q.; Zhang, X. M.; Tsai, D. P.; Bourouina, T.;Teng, J. H.; Zhang, X. H.; Guo, H. C.; Tanoto, H.; Mei, T.; Lo, G. Q.;Kwong, D. L. Adv. Mater. 2011, 23, 1792-1796.

(11) Prasanna, S.; Spearing, S. M. J. Microelectromech. S. 2007, 16,248-259.

(12) Lapine M.; Powell D.; Gorkunov M.; Shadrivov I.; Marques R.;Kivshar Y. Appl. Phys. Lett. 2009, 95, 084105.

(13) Zhao R.; Tassin T.; Koschny T.; Soukoulis C. M.; Opt. Express 2010,18, 25665-25676.

1. A tunable metamaterial structure comprising a membrane having an areathat is subdivided into a plurality of strips extending in a firstdimension with neighboring strips being spaced apart in a seconddimension by gaps, wherein the area hosts a metamaterial formed by anarray of metamaterial elements which at least partially cover the areaof the strips and define a plurality of lattice parameters of themetamaterial, and wherein at least selected ones of the strips areshaped and dimensioned to permit their motion in response to a controlparameter, thereby to cause neighboring strips to move relative to eachother and thereby perturb at least one lattice parameter of themetamaterial.
 2. The structure of claim 1, wherein the membrane isprovided with contacts to permit at least a subset of the strips to beelectrically addressed with an electrical actuation signal which causesrelative movement between neighboring strips.
 3. The structure of claim2, wherein the contacts are arranged to apply mutually attractive andrepulsive electrostatic forces laterally between neighboring strips, sothat a first subset of the gaps widen and a second subset of the gapsinterleaved with the first subset narrow under application of theelectrical actuation signal.
 4. The structure of claim 2, wherein thecontacts are arranged to apply a current to at least a first subset ofthe strips, and wherein at least a subset of the strips are made of aplurality of layers of different materials with different thermalexpansion coefficients such that changes in temperature induced by thecurrent cause bowing of those strips out of the plane of the membrane.5. The structure of claim 1, wherein at least a first subset of thestrips are made of a plurality of layers of different materials withdifferent thermal expansion coefficients such that changes intemperature cause bowing of those strips out of the plane of themembrane.
 6. The structure of claim 1, wherein a first subset and asecond subset of strips are at least partially covered by metamaterialelements configured to exert mutually attractive and/or repulsivelateral electromagnetic forces on one other when excited with anelectromagnetic wave of an appropriate frequency, such that a firstsubset of gaps widens and a second subset of gaps interleaved with thefirst subset narrows under application of the electromagnetic wave. 7.The structure of claim 1, wherein the strips have more flexible endportions.
 8. The structure of claim 7, wherein the more flexible endportions are formed as folded structures.
 9. The structure of claim 1,wherein at least selected ones of the strips have lateral protrusionsfacing into the gaps to inhibit large area contact between neighboringstrips.
 10. The structure of claim 1, wherein the strips are formed asfolded structures.
 11. The structure of claim 1, wherein the strips havea periodicity in the second dimension matched to a lattice parameter ofthe metamaterial in the second dimension.
 12. The structure of claim 11,wherein the matching is a one-to-one matching.
 13. The structure ofclaim 1, wherein the lattice parameters of the metamaterial are smallerthan at least one of 2000 nm, 1500 nm, 1250 nm, 1000 nm, 750 nm, 500 nmand 250 nm.
 14. A tunable metamaterial device comprising a structure asclaimed in claim 1 and a device controller operable to set the controlparameter.
 15. A method of operating a tunable metamaterial structuredevice, the method comprising: providing a membrane having an area thatis subdivided into a plurality of strips extending in a first dimensionwith neighboring strips being spaced apart in a second dimension bygaps, wherein the area hosts a metamaterial formed by an array ofmetamaterial elements which at least partially cover the area of thestrips and define a plurality of lattice parameters of the metamaterial;and changing a control parameter to cause neighboring strips to moverelative to each other and thereby perturb at least one latticeparameter of the metamaterial.
 16. The method of claim 15, wherein themembrane is provided with contacts to permit at least a subset of thestrips to be electrically addressed with an electrical actuation signalwhich causes relative movement between neighboring strips.
 17. Themethod of claim 15, wherein at least a first subset of the strips aremade of a plurality of layers of different materials with differentthermal expansion coefficients such that changes in temperature causebowing of those strips out of the plane of the membrane, and whereinchanging a control parameter comprises applying an electromagnetic waveto the device to cause a change in temperature.
 18. An optical devicefor modifying an optical beam input to the device, the device comprisinga tunable metamaterial structure according to claim
 1. 19. A temperaturesensor comprising: a tunable metamaterial structure according to claim5; an optical source operable to produce an optical beam incident ontothe tunable metamaterial structure; and an optical detector operable toreceive the optical beam from the tunable metamaterial structure anddetermine a temperature at the tunable metamaterial structure bycomparing the received optical beam and the incident optical beam.